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Any universe can be expressed using a suitable topology containing points.

At least the following (coherent) definitions exist for the multiverse (there can be more/others):

1. Topological disconnected universes

Universes which could be very much the same as ours, and could have the same or similar topology, but with the property that none of the points of such a universe is connected to any of the points of our universe.

2. Everet universes (parallel worlds)

Based on an interpretation of Quantum physics, in which every time a 'measurement' ("collapse of the wave function") takes place, immediately the world is split (in every point of spacetime) in all the possible outcomes of that measurement. All these universes have an independent existence.

All these "parallel" universes have the property that they have at least one point that is connected to at least one point of our universe, or another universe of this set (the parallel universes branche themselves also).

3. Tegmark universes (mathematical structures)

Every possible mathematical structure exists as a seperate universe. Our own is just one of such universes, with the property that it contains self-aware structures.

It can be concluded that all such universes are independent and disconnected from each other.

A mathematical structure is or has not necessary a topology with points, which fall a bit outside our definition.

4. Inflationary universes

Universes based on the cosmological inflation paradigm.

In the topological sense all these universes are connected to our universe. Even if they are called multiverses, in fact they are just part of the same universe (having a common topological space).

Multiverse just extends the definition of the universe.

Basic question

What topological requirements are there to regard a 'multiverse' as "existent", based on the scientific method (ie. the invisible elf sitting on my desk which does not interact with anything in the universe, can be said to not-exist).

Other questions of interest

- Topology that contains 'gaps'?
- Topologies that are not simply connected (for example: multiple connected in at least one point)
- Topologies that have boundaries/edges
- Other 'strange' topological properties

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# Ontological & topological issues wrt. the 'multiverse'

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